Tony Hayward, then chief executive of BP, answers questions from the media in 2010 after the Gulf of Mexico oil spill.
Photograph: John Moore/Getty Images

BP will face a maximum fine of $13.7bn under the Clean Water Act for its Gulf of Mexico oil spill in 2010, several billion less than feared.

Federal magistrate Carl Barbier ruled on Thursday that the size of the spill from the Deepwater Horizon drilling rig, the worst offshore spill in US history, was smaller than the government had claimed.

He said that it amounted to 3.19m barrels, well below the government’s estimate of 4.09m barrels, which could have led to penalties of up to $17.6bn.

US-listed shares of BP rose about 1% to $36.20 in after-hours trading as investors worried about the size of potential penalties breathed a sigh of relief.

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Under a ruling of gross negligence, Barbier issued in September, BP could be fined a statutory limit of up to $4,300 for each barrel spilled, though he has authority to assign lower penalties.

A simple negligence ruling, which BP sought, caps the maximum fine at $1,100 per barrel.

In his ruling on Thursday, Barbier said BP’s response to the disaster was not grossly negligent, but stuck to his earlier opinion that it was grossly negligent leading up to the blowout at the Macondo well. Penalties will be assigned after the third and final phase of the company’s non-jury trial, which starts on Tuesday in New Orleans.

BP lawyers are expected to argue for a small fine per barrel. A spokesman for the company said: “BP believes that considering all the statutory penalty factors together weighs in favour of a penalty at the lower end of the statutory range.” The first two phases of the trial, which concerned the degree of negligence and the size of the spill, have concluded.

The Clean Water Act penalties would come on top of more than $42bn the oil major has set aside or spent for clean-up, compensation and fines. About 810,000 barrels were collected during clean-up.

Even after the Clean Water Act fines are set, BP may face other bills from a lengthy Natural Resources Damage Assessment – which could require the company to carry out or fund environmental restoration work in the Gulf – as well as other claims.